Unison commissioned the Centre for Public Services to probe the partnership's performance because there was 'a great deal of disquiet among the staff', centre director Dexter Whitfield said.
This move followed criticisms of the partnership by the Audit Commission in its audit letter for 2004.
The£267m partnership began in 2001 and is due to run for 12 years. It covers finance, IT, human resources, school support services, and contract and facilities management. Some 550 county staff transferred to it.
The audit letter said Bedfordshire's 'inability to prepare timely, supportable statements of account is indicative of an inability to manage its financial position effectively'.
It added: 'The strategic partnership is not delivering improvements in services.'
Auditors ordered the council to identify the problems 'arising from the arrangements with HBS' and prepare an action plan. The council is expected to debate this next month.
A council spokesperson said: 'Last year we completed a self-assessment process which showed changes are required.'